Abstract A dependent variable is some unknown function of independent variables plus an error component. If the magnitude of the error could be estimated with minimal assumptions about the underlying functional dependence, then this could be used to judge goodness-of-fit and as a means of selecting a subset of the independent variables which best determine the dependent variable. We propose a procedure for this purpose which is based on a data-directed partitioning of the space into subregions and a fitting of the function in each subregion. The behavior of the procedure is heuristically discussed and illustrated by some simulation examples.